Modal Decomposition of Feedback Delay Networks

Sebastian J Schlecht, Emanuël A P Habets

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Feedback delay networks (FDNs) belong to a general class of recursive filters which are widely used in sound synthesis and physical modeling applications. We present a numerical technique to compute the modal decomposition of the FDN transfer function. The proposed pole finding algorithm is based on the Ehrlich-Aberth iteration for matrix polynomials and has improved computational performance of up to three orders of magnitude compared to a scalar polynomial root finder. The computational performance is further improved by bounds on the pole location and an approximate iteration step. We demonstrate how explicit knowledge of the FDN's modal behavior facilitates analysis and improvements for artificial reverberation. The statistical distribution of mode frequency and residue magnitudes demonstrate that relatively few modes contribute a large portion of impulse response energy.
Original languageEnglish
Pages (from-to)5340-5351
JournalIEEE Transactions on Signal Processing
Issue number20
Publication statusPublished - 2019
MoE publication typeA1 Journal article-refereed


  • Feedback delay network
  • modal synthesis
  • artificial reverberation
  • matrix polynomial
  • Ehrlich-Aberth iteration


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